Question

Given the parent function f(x) = x^2 describe the translation of the function y=(.2x)^2?

Answer 1

Option C.

Explanation:

Let
`f(x) = x ^ 2` be a quadratic function

Then we do the function
`y = f(bx) = (bx) ^ 2`

Where b is a real number.

If
`b> 1` then the function
`y = (bx) ^ 2` represents a horizontal compression of the function
`y = x ^ 2`

If
`0 <b <1` Then the function
`y = (bx) ^ 2` represents a horizontal expansion compression of the function
`y = x ^ 2` by a factor of
`(1)/(b)`

In this case, the equation is:

`y = (0.2x) ^ 2` Then:

`b = 0.2`

`0 <b <1`

Thus

`y = (0.2x) ^ 2` is a horizontal expansion of the function
`y = x ^ 2` by a factor of
`(1)/(0.2) = 5`.

The correct option is: Option C